Analysis of localized shear deformation of ductile metal based on gradient-dependent plasticity

1　INTRODUCTIONFailureprocessofmaterialsisparticularlycom plex ,whichisaprobleminvolvedinmulti scaleandmanydisciplines .Thoughscientistsfrommanycoun trieshavecontributedsomeimportantresultsfortheprobleminrecentyears ,furtherinvestigationsbyme chanicalscientists ,physicistsandmaterialscientistsarenecessarytoobtainafullunderstandingofthefailuremechanisms .Especiallyinlast 2 0 years ,asamechanismofprogressivefailure ,theproblemoflocalizationhasat tractedtopicinterest .Asaconsequenceofsofteni…     

Effects of constitutive parameters on adiabatic shear localization for ductile metal based on JOHNSON-COOK and gradient plasticity models

1Introduction Adiabatic shear band(ASB)is a very narrow zone with a high concentration of shear strain.It is believed that ASB is formed by a process of thermo-mechanical instability.ASB can be observed in the process of dynamic deformation of various fer…     

Phenomenon of transformed adiabatic shear band surrounded by deformed adiabatic shear band of ductile metal

The coexistent phenomenon of deformed and transformed adiabatic shear bands（ASBs） of ductile metal was analyzed using the JOHNSON-COOK model and gradient-dependent plasticity（GDP）. The effects of melting point, density, heat capacity and work to heat conversion factor were investigated. Higher work to heat conversion factor, lower density, lower heat capacity and higher melting point lead to wider transformed ASB and higher local plastic shear deformation between deformed and transformed ASBs. Higher work to heat conversion factor, lower density, lower heat capacity and lower melting point cause higher local plastic shear deformation in the deformed ASB. Three reasons for the scatter in experimental data on the ASB width were pointed out and the advantages of the work were discussed. If the transformed ASB width is used to back-calculate the internal length parameter in the GDP, undoubtedly, the parameter will be extremely underestimated.     

A method for calculating damage evolution in adiabatic shear band of titanium alloy

A method for calculating the evolution of the local damage variable at the adiabatic shear band (ASB) center was proposed. In the present method, the JOHNSON-COOK model and the nonlocal theory were adopted, and the damage variable formula applicable for the bilinear (linearly elastic and strain-softening) constitutive relation was further generalized to consider the plastic deformation occurring in the strain-hardening stage. Aiming at Ti-6Al-4V, the effect of strain rate on the evolution of the local damage variable at the ASB center was investigated. In addition, a parametric study was carried out, including the effects of strain-hardening exponent, strain rate sensitive coefficient, thermal-softening exponent, static shear strength, strain-hardening modulus, shear elastic modulus, work to heat conversion factor, melting temperature and initial temperature. The damage extent at the ASB center in the radial collapse experiment was assessed. It is found that at higher strain rates the damage in the ASB becomes more serious at the same average plastic shear strain of the ASB.     

Localized shear deformation during shear band propagation in titanium considering interactions among microstructures

Closed-form analytical solutions of plastic shear strain and relative plastic shear displacement during shear band propagation are proposed under dynamic loadings based on gradient-dependent plasticity considering the effect of microstructures due to heterogeneous texture of Ti. According to the differences in shear stress levels, Ti specimen is divided into three regions: residual region, strain-softening region and elastic region. Well-developed shear band is formed in the residual region and the relative plastic shear displacement no longer increases. In the normal and tangential directions, the plastic strain and the displacement are nonuniform in the strain-softening region.At the tip of shear band, the shear stress acting on the band is increased to shear strength from the elastic state and the shear localization just occurs. Prior to the tip, Ti remains elastic. At higher strain rates, the extent of plastic strain concentration is greater than that under static loading. Higher strain rate increases the relative plastic shear displacement. The present analytical solution for evolution or propagation of shear localization under nonuniform shear stress can better reproduce the observed localized characteristics for many kinds of ductile metals.     

Quantitative calculation of local shear deformation in adiabatic shear band for Ti-6Al-4V

JOHNSON-COOK（J-C） model was used to calculate flow shear stress-shear strain curve for Ti-6Al-4V in dynamic torsion test. The predicted curve was compared with experimental result. Gradient-dependent plasticity（GDP） was introduced into J-C model and GDP was involved in the measured flow shear stress-shear strain curve, respectively, to calculate the distribution of local total shear deformation（LTSD） in adiabatic shear band（ASB）. The predicted LTSDs at different flow shear stresses were compared with experimental measurements. J-C model can well predict the flow shear stress-shear strain curve in strain-hardening stage and in strain-softening stage where flow shear stress slowly decreases. Beyond the occurrence of ASB, with a decrease of flow shear stress, the increase of local plastic shear deformation in ASB is faster than the decrease of elastic shear deformation, leading to more and more apparent shear localization. According to the measured flow shear stress-shear strain curve and GDP, the calculated LTSDs in ASB are lower than experimental results. At earlier stage of ASB, though J-C model overestimates the flow shear stress at the same shear strain, the model can reasonably assess the LTSDs in ASB. According to the measured flow shear stress-shear strain curve and GDP, the calculated local plastic shear strains in ASB agree with experimental results except for the vicinity of shear fracture surface. In the strain-softening stage where flow shear stress sharply decreases, J-C model cannot be used. When flow shear stress decreases to a certain value, shear fracture takes place so that GDP cannot be used.     

考虑材料韧性损伤的中厚板半冲孔成形过程分析

为研究半冲孔成形过程中韧性损伤的演化以及部分工艺参数对成形质量的影响规律,本文在ABAQUS有限元模拟软件中建立了半冲孔轴对称有限元模型,并通过VUMAT用户子程序引入GTN(Gurson-Tvergaard-Needle-man)损伤模型,结合同时考虑空穴形状与体积变化影响的韧性断裂准则,进行弹塑性大变形有限元分析.基于该有限元模犁,预测了半冲孔工艺中静水压力、等效应力、等效应变、应力三轴度以及损伤断裂的产生和发展趋势,分析了反顶力、压边力和冲裁间隙对零件的影响规律,并与实验结果进行对比分析,验证了数值模拟的准确性.     

Calculation of temperature distribution in adiabatic shear band based on gradient-dependent plasticity

A method for calculation of temperature distribution in adiabatic shear band is proposed in terms of gradient-dependent plasticity where the characteristic length describes the interactions and interplaying among microstructures. First, the increment of the plastic shear strain distribution in adiabatic shear band is obtained based on gradient-dependent plasticity. Then, the plastic work distribution is derived according to the current flow shear stress and the obtained increment of plastic shear strain distribution. In the light of the well-known assumption that 90% of plastic work is converted into the heat resulting in increase in temperature in adiabatic shear band, the increment of the temperature distribution is presented. Next, the average temperature increment in the shear band is calculated to compute the change in flow shear stress due to the thermal softening effect. After the actual flow shear stress considering the thermal softening effect is obtained according to the Johnson-Cook constitutive relation, the increment of the plastic shear strain distribution, the plastic work and the temperature in the next time step are recalculated until the total time is consumed. Summing the temperature distribution leads to rise in the total temperature distribution. The present calculated maximum temperature in adiabatic shear band in titanium agrees with the experimental observations. Moreover, the temperature profiles for different flow shear stresses are qualitatively consistent with experimental and numerical results. Effects of some related parameters on the temperature distribution are also predicted.     

锯齿形切屑绝热剪切塑性变形

通过正交切削实验获得不同切削速度下的切屑,在扫描电镜下测量不同切削速度下切屑的微观几何形态与仿真结果进行比较。结果表明,仿真模型较好模拟了切屑的微观几何形态。对钛合金切削加工过程中的锯齿形切屑形成过程进行了仿真,分析了锯齿形切屑形成过程中等效应力、等效应变、等效应变率的分布变化规律。     

Numerical analysis of shear deformation localization using a double-variable damage model

A double-variable damage model was introduced into the constitutive equations to demonstrate the effect of the material damage for the isotropic elastic, hardening, and damage states, and for the isothermal process. The shear damage variable D _s and the bulk damage variable D _b may be, respectively, used to describe the effect of shear damage and bulk damage for material properties without the superfluous constraint, D _b=D _s, that is found in the single-variable damage model. The double-variable damage model was implemented to form the finite element code for analyzing the effect of shear damage and bulk damage. In this article, two numerical simulation examples were completed to model the whole process of initiation and propagation of shear bands in an aluminum alloy. The numerical computational results are coincident with the experimental results.     

Nonlocal approach in evaluating strain localization behaviors of voided ductile materials

Finite element analysis of the strain localization behaviors of a voided ductile material has been performed using a non-local plasticity, in which the yield strength depends on both an equivalent plastic strain measure (hardening parameter) and Laplacian equivalent. The introduction of gradient terms to the yield function was found to play an important role in simulating the strain localization behavior of the voided ductile material. The effect of the mesh size and characteristic length on the strain localization were also investigated. An FEM simulation based on the proposed non-local plasticity revealed that the load-strain curves of the voided ductile material subjected to plane strain tension converges to one curve, regardless of the mesh size. In addition, the results using non-local plasticity also showed that the dependence of the deformation behavior of the material on the mesh size was much less sensitive than with classical local plasticity and could be successfully eliminated through the introduction of a large value for the characteristic length.     

Temperature distribution in adiabatic shear band for ductile metal based on JOHNSON-COOK and gradient plasticity models

1 Introduction Adiabatic shear localization is one of the most important deformation and failure mechanisms in some titanium alloys subjected to moderate and high shear strain rates. Adiabatic shear band(ASB) can be observed in various applications, such as metal forming, perforation, impact on structures, ballistic impact, machining, torsion, explosive fragmentation, grinding, interfacial friction, powder compaction and granular flow[1?15]. The formation of ASBs is often followed by ductile…     

楔横轧韧性损伤模型中Zener-Hollomon参数的确定

为将温度和应变速率耦合到现存的韧性断裂准则中,文章利用Gleeble3500热模拟机对45钢进行压缩实验,采用最小二乘法计算Zener-Hollomon参数中的变形激活能Q,得到了45钢在温度1050℃~1200℃、应变速率1s-1~100s-1下的材料流动应力方程,不仅为韧性损伤模型的建立奠定了基础,而且可为应用韧性断裂准则模拟楔横轧心部缺陷的有限元模拟中的材料模型,提供基础数据。     

金属板材成形中拉深损伤模拟的两种求解方法

讨论用数值模拟预测板材成形中发生拉深损伤破坏的两种不同的求解方法。第一种是采用完全耦合的弹塑性破坯模型的动力显式数值方法。基于状态参量的不可逆热力学过程 ,完全耦合的本构方程考虑各向同性强化和拉深。这些已引入有限元软件ABAQUS/E用于对金属成形的模拟。在数值技术方面 ,隐式积分方法被用来对本构方程的局部时间积分 ,动力显式技术用于求解总体平衡方程。第二种方案是采用简化的损伤模型的方法 ,被称为逆法 (InveseApprch)。I.A被限定在考虑各向同性强化和损伤的塑性全量理论基础上的简单的本构关系。做比例加载和临界损伤达到以后的损伤饱和假定 ,可以得到损伤演化方程的封闭解。这两种损伤模型在编程中的实施采用两种方式 :计算中考虑或不考虑损伤作用 ,也就是耦合的或非耦合的计算。文中给出一些算例来说明每种损伤模型的优点     

Analytical and experimental study of shear localization in chip formation in orthogonal machining

A simplified theory of instability of plastic flow is applied to analyze the formation of shear localized chips in orthogonal machining. A flow localization parameter is expressed in terms of associated cutting conditions and properties of the workpiece material. The analysis, which indicates the important parameters in the cutting process, is used to investigate the effect of cutting conditions on the onset of shear localization and the formation of adiabatic shear banding in metal cutting. Comparisons are made between the analysis and experiments in which the flow localization parameter is obtained for several workpiece materials. The results of this investigation seem to support the analysis and its potential benefits in analyzing and/or remedying problems associated with chip formation and temperature generated in metal cutting. Presently at Advanced Technology Center, Valenite, Inc., Madison Heights,MI 48071, USA     

韧性断裂准则及损伤模型在冲裁有限元模拟中的应用研究

在冲裁有限元模拟中,韧性断裂准则的选择会对冲裁件断面质量与尺寸精度产生很大影响。为了获得符合实际的模拟结果,进而优化冲裁工艺,重点研究了一些常用的韧性断裂判定依据,并从物理学角度阐述了韧性断裂机制。基于试验的韧性断裂准则,考虑了变形历史中的应力应变关系,使用由反求法确定的临界值来判定韧性断裂的发生与否。基于连续损伤力学建立的损伤模型,考虑了变形过程中损伤累积对材料本构关系的影响,能够更准确地描述断裂过程。此外,还分析了冲裁有限元模拟中的关键技术,如采用任意拉格朗日欧拉方法来解决网格畸变问题,使用单元分裂、单元分离与单元删除等技术来处理裂纹的萌发与扩展。探讨了目前韧性断裂模拟中存在问题以及未来发展方向。     

Role of shear band in texture control of Al-Mg alloys

Shear bands formed in Al-Mg alloys during cold rolling are nucleated on grain boundaries. Their mechanism of formation is different from that already proposed in the case of single crystals of the same alloy. Since recrystallized grains of non-cube orientations are nucleated on these shear bands during annealing, the development of cube recrystallization texture can be strongly suppressed by enhancing shear banding during cold rolling. Control of shear band thus provides a new fundamental technological tool to improve drawability of Al alloy sheets. In a microscopic scale, deformation in grain boundary regions also plays here a very important role, as in the case of the formation of {111}uvw recrystallization textures in low carbon steel sheets.     

Experimental and finite element simulation study of the adiabatic shear band phenomenon in cold heading process

This paper presents the outcomes of a comprehensive experimental, metallurgical and finite element (FE) simulation study to characterize the development of adiabatic shear band (ASB) phenomenon in steel cold heading (CH) process. The main objective of this work is to investigate the complex interplay of different process and material parameters on the ASB development stages inside the cold headed parts.In this work, the drop weight compression test (DWCT) was selected to simulate the CH process impact loads on specimens machined from 1038 steel and 1018 steel. Series of DWCTs were performed under different impact loading conditions. The goal of these tests is to achieve different deformation levels and introduce ASBs at different stages.To reach a full understanding of this complex phenomenon, the FE simulation analysis was used to support the metallurgical examination of the DWCT specimens. The FE analysis provided important details about the changes of different material and process parameters at the critical zones inside the ASBs.This study confirmed that the ASB is mainly a thermo-mechanically controlled phenomenon. The ASBs develop in three stages: homogeneous plastic strain, inhomogeneous plastic strain, and strain localization. The ASB development stage depends mainly on the status of the competition between the work hardening and the thermal and geometrical softening mechanisms inside the bands. The domination of the softening mechanisms at advanced levels of deformation triggers a self-catalytic strain localization and material strength degradation process that leads to failure inside the band.In general, the metallurgical and finite element analysis investigation revealed that under impact loads, three ASBs can develop simultaneously inside the cold headed parts; lower, upper and central ASBs. As the deformation continues; the development of the lower and upper bands slows down and contributes in the rapid development of the adjacent central ASB. This study confirmed that the ASB has a canonical structure which leads to an ASB that can experience different development stages along the same band simultaneously.This study proved that the shape and the type of ASBs in cold headed parts depend highly on material's properties. The metallurgical and finite element analysis revealed that the higher the strength of the tested steel, the easier to form a narrow ASB that reaches the localization stage at low deformation levels. In contrast, ductile steels experience wider ASBs when subjected to the same deformation levels. These bands require higher levels of deformation to reach the localization stage in comparison to higher strength steels.     

Evolution of shear texture according to shear strain ratio in rolled FCC metal sheets

The shear textures developed in the surface layer by rolling procedures consist mainly of {001}<110> and {111}<uvw> orientations in FCC metal sheets, but the orientation components of shear textures vary with the rolling conditions. That is, either a single orientation component or a mixture of components can be developed depending on the rolling conditions. The purpose of this study is to analyze the various shear deformation textures in rolled FCC metal sheets.